Cube Rotation

Question 1

Answer

Place the cube on one side and orient it according to the 4 directions. Move to the next position (other side) and so on to get all rotations.

Example:

Question 2

Answer

The die can fall on one of the 6 faces possible and be oriented according to 4 angles, or 24 possibilities. $$ 6 \times 4 = 24 $$

Question 3

Answer

There are 4 types of rotation of a dice:

- Rotation according to the diagonals

- Rotation along the axis connecting the centers of 2 opposite faces

- Rotation along the axis connecting the centers of 2 opposite edges

- Identity rotation (original stationary state)

Question 4

Answer

A cube whose faces are undifferentiated with 13 axes of symmetries:

- 3 axes pass through the centers of the faces, a cube has 6 faces, so 3 axes

- 6 axes pass through the centers of the opposite edges, a cube has 12 edges, so 6 axes

- 4 axes go through the opposite corners, a cube has 8 angles, so 4 axes

Dice Rotations